SSE2/PSIMD RAddStoreExpMinusMax micro-kernels
PiperOrigin-RevId: 291432270
diff --git a/src/f32-raddstoreexpminusmax/gen/sse2-p5-x12.c b/src/f32-raddstoreexpminusmax/gen/sse2-p5-x12.c
new file mode 100644
index 0000000..9f8cf69
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+++ b/src/f32-raddstoreexpminusmax/gen/sse2-p5-x12.c
@@ -0,0 +1,240 @@
+// Auto-generated file. Do not edit!
+// Template: src/f32-raddstoreexpminusmax/sse2-p5.c.in
+// Generator: tools/xngen
+//
+// Copyright 2019 Google LLC
+//
+// This source code is licensed under the BSD-style license found in the
+// LICENSE file in the root directory of this source tree.
+
+#include <assert.h>
+
+#include <emmintrin.h>
+
+#include <xnnpack/common.h>
+#include <xnnpack/raddstoreexpminusmax.h>
+
+
+void xnn_f32_raddstoreexpminusmax_ukernel__sse2_p5_x12(
+ size_t elements,
+ const float* input,
+ float* output,
+ float* sum,
+ float max)
+{
+ assert(elements % sizeof(float) == 0);
+
+ const __m128 vmagic_bias = _mm_set1_ps(0x1.8000FEp23f);
+ // The smallest x for which expf(x) is normalized.
+ const __m128 vdenorm_cutoff = _mm_set1_ps(-0x1.5D589Ep6f);
+ const __m128 vlog2e = _mm_set1_ps(0x1.715476p+0f);
+ // Last 7 bits are zeroes
+ const __m128 vminus_ln2_hi = _mm_set1_ps(-0x1.62E400p-1f);
+ const __m128 vminus_ln2_lo = _mm_set1_ps(-0x1.7F7D1Cp-20f);
+
+ const __m128 vc1 = _mm_set1_ps(0x1.FFFFF6p-1f);
+ const __m128 vc2 = _mm_set1_ps(0x1.FFFDC6p-2f);
+ const __m128 vc3 = _mm_set1_ps(0x1.555A80p-3f);
+ const __m128 vc4 = _mm_set1_ps(0x1.573A1Ap-5f);
+ const __m128 vc5 = _mm_set1_ps(0x1.0F9F9Cp-7f);
+
+ const __m128 vi_max = _mm_set1_ps(max);
+
+ __m128 vacc0 = _mm_setzero_ps();
+ for (; elements >= 12 * sizeof(float); elements -= 12 * sizeof(float)) {
+ // Load 12 (3x4) inputs at a time.
+ const __m128 vi0123 = _mm_loadu_ps(input);
+ const __m128 vi4567 = _mm_loadu_ps(input + 4);
+ const __m128 vi89AB = _mm_loadu_ps(input + 8);
+ input += 12;
+
+ // Subtract maximum input x := i - i_max. This implies x <= 0.
+ const __m128 vx0123 = _mm_sub_ps(vi0123, vi_max);
+ const __m128 vx4567 = _mm_sub_ps(vi4567, vi_max);
+ const __m128 vx89AB = _mm_sub_ps(vi89AB, vi_max);
+
+ // Compute reduced argument elements := round(x / log(2)).
+ __m128 vn0123 = _mm_add_ps(_mm_mul_ps(vx0123, vlog2e), vmagic_bias);
+ __m128 vn4567 = _mm_add_ps(_mm_mul_ps(vx4567, vlog2e), vmagic_bias);
+ __m128 vn89AB = _mm_add_ps(_mm_mul_ps(vx89AB, vlog2e), vmagic_bias);
+
+ // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
+ // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
+ const __m128 vs0123 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn0123), 23));
+ const __m128 vs4567 = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn4567), 23));
+ const __m128 vs89AB = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn89AB), 23));
+
+ // Subtract the large number back to get final elements := round(x / log(2)).
+ vn0123 = _mm_sub_ps(vn0123, vmagic_bias);
+ vn4567 = _mm_sub_ps(vn4567, vmagic_bias);
+ vn89AB = _mm_sub_ps(vn89AB, vmagic_bias);
+
+ // Compute reduced argument t := x - elements * log(2).
+ // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
+ __m128 vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_hi), vx0123);
+ __m128 vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_hi), vx4567);
+ __m128 vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_hi), vx89AB);
+
+ vt0123 = _mm_add_ps(_mm_mul_ps(vn0123, vminus_ln2_lo), vt0123);
+ vt4567 = _mm_add_ps(_mm_mul_ps(vn4567, vminus_ln2_lo), vt4567);
+ vt89AB = _mm_add_ps(_mm_mul_ps(vn89AB, vminus_ln2_lo), vt89AB);
+
+ // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
+ __m128 vp0123 = _mm_add_ps(_mm_mul_ps(vc5, vt0123), vc4);
+ __m128 vp4567 = _mm_add_ps(_mm_mul_ps(vc5, vt4567), vc4);
+ __m128 vp89AB = _mm_add_ps(_mm_mul_ps(vc5, vt89AB), vc4);
+
+ vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc3);
+ vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc3);
+ vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc3);
+
+ vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc2);
+ vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc2);
+ vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc2);
+
+ vp0123 = _mm_add_ps(_mm_mul_ps(vp0123, vt0123), vc1);
+ vp4567 = _mm_add_ps(_mm_mul_ps(vp4567, vt4567), vc1);
+ vp89AB = _mm_add_ps(_mm_mul_ps(vp89AB, vt89AB), vc1);
+
+ // Reconstruct the final f value:
+ // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
+ // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
+ // = s + (t * s) * p
+ vt0123 = _mm_mul_ps(vt0123, vs0123);
+ vt4567 = _mm_mul_ps(vt4567, vs4567);
+ vt89AB = _mm_mul_ps(vt89AB, vs89AB);
+
+ __m128 vf0123 = _mm_add_ps(_mm_mul_ps(vt0123, vp0123), vs0123);
+ __m128 vf4567 = _mm_add_ps(_mm_mul_ps(vt4567, vp4567), vs4567);
+ __m128 vf89AB = _mm_add_ps(_mm_mul_ps(vt89AB, vp89AB), vs89AB);
+
+ // For inputs below zero cutoff, replace output with +0.0f.
+ // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
+ vf0123 = _mm_andnot_ps(_mm_cmplt_ps(vx0123, vdenorm_cutoff), vf0123);
+ vf4567 = _mm_andnot_ps(_mm_cmplt_ps(vx4567, vdenorm_cutoff), vf4567);
+ vf89AB = _mm_andnot_ps(_mm_cmplt_ps(vx89AB, vdenorm_cutoff), vf89AB);
+
+ // Store 12 (3x4) outputs at a time.
+ _mm_storeu_ps(output, vf0123);
+ _mm_storeu_ps(output + 4, vf4567);
+ _mm_storeu_ps(output + 8, vf89AB);
+ output += 12;
+
+ // Accumulate computed exponents.
+ vacc0 = _mm_add_ps(vacc0, vf0123);
+ vacc0 = _mm_add_ps(vacc0, vf4567);
+ vacc0 = _mm_add_ps(vacc0, vf89AB);
+ }
+
+ __m128 vacc = vacc0;
+ for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
+ // Load 4 inputs at a time.
+ const __m128 vi = _mm_loadu_ps(input);
+ input += 4;
+
+ // Subtract maximum input x := i - i_max. This implies x <= 0.
+ const __m128 vx = _mm_sub_ps(vi, vi_max);
+
+ // Compute reduced argument elements := round(x / log(2)).
+ __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
+
+ // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
+ // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
+ const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
+
+ // Subtract the large number back to get final elements := round(x / log(2)).
+ vn = _mm_sub_ps(vn, vmagic_bias);
+
+ // Compute reduced argument t := x - elements * log(2).
+ // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
+ __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
+ vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
+
+ // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
+ __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
+ vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
+ vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
+ vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
+
+ // Reconstruct the final f value:
+ // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
+ // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
+ // = s + (t * s) * p
+ vt = _mm_mul_ps(vt, vs);
+ __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
+
+ // For inputs below zero cutoff, replace output with +0.0f.
+ // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
+ vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
+
+ // Store 4 outputs at a time.
+ _mm_storeu_ps(output, vf);
+ output += 4;
+
+ // Accumulate computed exponents.
+ vacc = _mm_add_ps(vacc, vf);
+ }
+ if (elements != 0) {
+ assert(elements >= 1 * sizeof(float));
+ assert(elements <= 3 * sizeof(float));
+ // Load 4 inputs at a time.
+ const __m128 vi = _mm_loadu_ps(input);
+
+ // Subtract maximum input x := i - i_max. This implies x <= 0.
+ const __m128 vx = _mm_sub_ps(vi, vi_max);
+
+ // Compute reduced argument elements := round(x / log(2)).
+ __m128 vn = _mm_add_ps(_mm_mul_ps(vx, vlog2e), vmagic_bias);
+
+ // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
+ // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
+ const __m128 vs = _mm_castsi128_ps(_mm_slli_epi32(_mm_castps_si128(vn), 23));
+
+ // Subtract the large number back to get final elements := round(x / log(2)).
+ vn = _mm_sub_ps(vn, vmagic_bias);
+
+ // Compute reduced argument t := x - elements * log(2).
+ // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
+ __m128 vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_hi), vx);
+ vt = _mm_add_ps(_mm_mul_ps(vn, vminus_ln2_lo), vt);
+
+ // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
+ __m128 vp = _mm_add_ps(_mm_mul_ps(vc5, vt), vc4);
+ vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc3);
+ vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc2);
+ vp = _mm_add_ps(_mm_mul_ps(vp, vt), vc1);
+
+ // Reconstruct the final f value:
+ // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
+ // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
+ // = s + (t * s) * p
+ vt = _mm_mul_ps(vt, vs);
+ __m128 vf = _mm_add_ps(_mm_mul_ps(vt, vp), vs);
+
+ // For inputs below zero cutoff, replace output with +0.0f.
+ // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
+ vf = _mm_andnot_ps(_mm_cmplt_ps(vx, vdenorm_cutoff), vf);
+
+ if (elements & (2 * sizeof(float))) {
+ // Store 2 outputs at a time.
+ _mm_storel_pi((__m64*) output, vf);
+ output += 2;
+
+ // Accumulate 2 computed exponents.
+ vacc = _mm_add_ps(vacc, _mm_movelh_ps(vf, _mm_setzero_ps()));
+
+ vf = _mm_movehl_ps(vf, vf);
+ }
+ if (elements & (1 * sizeof(float))) {
+ // Store 1 output at a time.
+ _mm_store_ss(output, vf);
+
+ // Accumulate 1 computed exponent.
+ vacc = _mm_add_ss(vacc, vf);
+ }
+ }
+ // Reduce 4 elements in the SIMD register
+ vacc = _mm_add_ps(vacc, _mm_movehl_ps(vacc, vacc));
+ vacc = _mm_add_ss(vacc, _mm_shuffle_ps(vacc, vacc, _MM_SHUFFLE(2, 3, 0, 1)));
+ _mm_store_ss(sum, vacc);
+}